一种基于犹豫模糊粗糙集的工厂代储器材品种决策方法

doi:10.12305/j.issn.1001-506X.2026.01.21

Abstract

Abstract:

Aiming at the characteristics of the factory storage equipment guarantee mode and the hesitant fuzzy feature of decision-making information, it is difficult to achieve attribute reduction and rule extraction using traditional equipment variety decision-making methods. Firstly, a equipment variety decision-making method based on hesitant fuzzy rough sets is proposed. Analyze the influencing factors of factory storage equipment variety decision-making from the aspects of production cycle, criticality, storage requirements, economy, consumption, universality, and modernization level of guarantee equipment. Secondly, an incomplete information extension method based on decision-making habits is proposed. Finally, constructed a equipment attribute reduction and rule extraction model based on similarity-derived fuzzy equivalence relation. A certain storage equipment factory is selected as a case study, and verified the effectiveness of the proposed method. The proposed method effectively completed the selection of storage equipment varieties.

Key words: hesitant fuzzy set, rough set, variety selection, attribute reduction, decision-making rule

CLC Number:

E 92

Zhiqiang CUI, Hongli JIA, Lili GAO, Bing HAO. Decision-making method based on hesitant fuzzy rough set for the variety of equipment stored on behalf of the factory[J]. Systems Engineering and Electronics, 2026, 48(1): 235-248.

Figures/Tables 13

Table 1

Fig.1

Fig.2

Fig.3

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

Table 10

Decision rules for factory stocking of devices"

条件	决策	说明
$ \widetilde r_{1,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{1,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{1,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_1} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{2,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{2,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{2,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_2} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{3,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{3,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{3,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_3} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{4,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{4,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{4,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_4} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{7,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{7,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{7,{x_k}}^{{c_3}} \geqslant 0.775 $	配置	$ {x_7} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_1^d) $
$ \widetilde r_{8,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{8,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{8,{x_k}}^{{c_3}} \geqslant 0.775 $	不配置	$ {x_8} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_0^d) $
$ \widetilde r_{10,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{10,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{10,{x_k}}^{{c_3}} \geqslant 0.775 $	不配置	$ {x_{10}} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_0^d) $
$ \widetilde r_{11,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{11,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{11,{x_k}}^{{c_3}} \geqslant 0.775 $	不配置	$ {x_{11}} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_0^d) $
$ \widetilde r_{12,{x_k}}^{{c_1}} \geqslant 0.775 \wedge \widetilde r_{12,{x_k}}^{{c_2}} \geqslant 0.775 \wedge \widetilde r_{12,{x_k}}^{{c_3}} \geqslant 0.775 $	不配置	$ {x_{12}} \in \underline {\Re _{{c_1} \cup {c_2} \cup {c_3}}^\lambda } (X_0^d) $

Table 10

References 31

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器材类型	确定方法
关键件	器材发生故障或损坏将导致装备无法完成预定任务、丧失关键功能，甚至导致整个装备系统停机
重要件	器材发生故障或损坏将显著影响装备运转和性能发挥，降低任务执行效率或部分功能受限，但不会导致整个装备系统停机
一般件	器材发生故障或损坏将导致装备性能轻微降低，对装备的正常运行影响较小，通常不会影响任务的完成或装备的基本功能

器材品种	生产周期/月	器材价格/元	保障装备使用时间/年
x₁	15	5 099 302	4
x₂	+	3 800 000	1
x₃	12	1 855 400	3
x₄	5	1 469 000	4
x₅	4	357 082.5	8
x₆	6	51 250	8
x₇	+	45 000	1
x₈	1	43 651.88	4
x₉	+	13 500	1
x₁₀	2	204.75	25
x₁₁	1	54	16
x₁₂	2	46.2	9

保障装备使用时间/年	赋值
1	0.9
2	0.8
3	0.8
4	0.7
5	0.7
6~10	0.6
11~15	0.4
16~20	0.2
>20	0.1

论域	生产周期	关键程度	存储要求	经济性	消耗量	通用性	使用程度	是否存储
x₁	0.9	0.85，0.9，0.95	0.5，0.5，0.6	0.95	0.85，0.9，0.9	0.85，0.9，0.95	0.7	1
x₂	0.9，*，0.95	0.85，*，0.95	0.5，0.5，0.6	0.95	0.85，0.9，0.9	0.85，*，0.95	0.9	1
x₃	0.75	0.85，0.9，0.95	0.5，0.6，0.65	0.9	0.8，0.85，*	0.85，0.9，0.95	0.8	1
x₄	0.3	0.5，0.7，0.8	*，0.85，0.9	0.9	0.6，0.7，0.7	0.6，0.7，0.7	0.7	1
x₅	0.3	0.4，0.5，0.7	0.1，0.15，0.2	0.8	0.8，0.8，0.9	0.1，0.2，0.2	0.6	0
x₆	0.35	0.4，0.6，0.7	0.3，0.4，0.45	0.75	0.7，*，0.8	0.6，0.6，0.7	0.6	1
x₇	0.3，0.3，0.4	0.45，0.5，0.7	0.8，*，0.9	0.7	0.6，0.7，0.7	0.6，0.7，0.7	0.9	1
x₈	0.05	0.2，0.3，0.35	0.2，0.3，0.35	0.7	0.25，0.3，0.3	0.4，0.5，0.5	0.7	0
x₉	0.2，0.2，0.3	0.6，0.7，0.75	0.5，0.55，0.7	0.5	0.5，0.5，0.6	0.2，0.3，0.3	0.9	1
x₁₀	0.1	0.2，*，0.3	0.2，0.3，0.35	0.1	0.2，0.2，0.3	0.1，0.1，0.2	0.1	0
x₁₁	0.05	0.1，0.2，0.3	0.05，0.1，0.15	0.05	0.15，0.2，0.2	*，0.1，0.1	0.2	0
x₁₂	0.1	0.1，0.3，0.35	0.2，0.3，0.35	0.05	0.2，0.2，0.3	0.4，0.5，0.5	0.6	0

论域	生产周期	关键程度	存储要求	经济性	消耗量	通用性	使用程度	是否存储
x₁	0.9	0.85，0.9，0.95	0.5，0.5，0.6	0.95	0.85，0.9，0.9	0.85，0.9，0.95	0.7	1
x₂	0.9，0.9，0.95	0.85，0.9，0.95	0.5，0.5，0.6	0.95	0.85，0.9，0.9	0.85，0.92，0.95	0.9	1
x₃	0.75	0.85，0.9，0.95	0.5，0.6，0.65	0.9	0.8，0.85，0.9	0.85，0.9，0.95	0.8	1
x₄	0.3	0.5，0.7，0.8	0.8，0.85，0.9	0.9	0.6，0.7，0.7	0.6，0.7，0.7	0.7	1
x₅	0.3	0.4，0.5，0.7	0.1，0.15，0.2	0.8	0.8，0.8，0.9	0.1，0.2，0.2	0.6	0
x₆	0.35	0.4，0.6，0.7	0.3，0.4，0.45	0.75	0.7，0.75，0.8	0.6，0.6，0.7	0.6	1
x₇	0.3，0.3，0.4	0.45，0.5，0.7	0.8，0.85，0.9	0.7	0.6，0.7，0.7	0.6，0.7，0.7	0.9	1
x₈	0.05	0.2，0.3，0.35	0.2，0.3，0.35	0.7	0.25，0.3，0.3	0.4，0.5，0.5	0.7	0
x₉	0.2，0.2，0.3	0.6，0.7，0.75	0.5，0.55，0.7	0.5	0.5，0.5，0.6	0.2，0.3，0.3	0.9	1
x₁₀	0.1	0.2，0.25，0.3	0.2，0.3，0.35	0.1	0.2，0.2，0.3	0.1，0.1，0.2	0.1	0
x₁₁	0.05	0.1，0.2，0.3	0.05，0.1，0.15	0.05	0.15，0.2，0.2	0.1，0.1，0.1	0.2	0
x₁₂	0.1	0.1，0.3，0.35	0.2，0.3，0.35	0.05	0.2，0.2，0.3	0.4，0.5，0.5	0.6	0

Decision-making method based on hesitant fuzzy rough set for the variety of equipment stored on behalf of the factory

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论域（U）	关键程度	存储要求	通用性	是否存储
x₁	0.85，0.9，0.95	0.5，0.5，0.6	0.85，0.9，0.95	1
x₂	0.85，0.9，0.95	0.5，0.5，0.6	0.85，0.9，0.95	1
x₃	0.85，0.9，0.95	0.5，0.6，0.65	0.85，0.9，0.95	1
x₄	0.5，0.7，0.8	0.8，0.85，0.9	0.6，0.7，0.7	1
x₅	0.4，0.5，0.7	0.1，0.15，0.2	0.1，0.2，0.2	0
x₆	0.4，0.6，0.7	0.3，0.4，0.45	0.6，0.6，0.7	1
x₇	0.45，0.5，0.7	0.8，0.85，0.9	0.6，0.7，0.7	1
x₈	0.2，0.3，0.35	0.2，0.3，0.35	0.4，0.5，0.5	0
x₉	0.6，0.7，0.75	0.5，0.55，0.7	0.2，0.3，0.3	1
x₁₀	0.2，0.25，0.3	0.2，0.3，0.35	0.1，0.1，0.2	0
x₁₁	0.1，0.2，0.3	0.1，0.15，0.5	0.1，0.1，0.1	0
x₁₂	0.1，0.3，0.35	0.2，0.3，0.35	0.4，0.5，0.5	0

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